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I have to do a convolution of a periodic signal with a Dirac impulse.

$\quad \quad x(t)=\sin(π\, t)(u(t)−u(t−2))$
$\quad \quad h(t)=u(t−1)−u(t−3)$

The first is a periodic signal that intersects the x-axis at points 0, 1, 2, .... The second is a rectangle (Dirac impulse) that intersects the x-axis at points 1 and 3.

For $t−1 < 0$ and $t−3 > 0$ the convolution doesn't exist.

I think the convolution is $\int_0^1\sin \pi\, (t-\tau)\, dt - \int_1^{t-1}\sin \pi\, (t-\tau)\, dt$, but my book gives $\int_0^1\sin \pi\, t\, dt$

Could someone tell me why he cancel -τ, and how to do this example without using a Fourier transform? Sorry for my terrible english, but i'm italian.

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    $\begingroup$ Hi ! Are you sure this is a Mathematica related problem ? $\endgroup$
    – Sektor
    Nov 2, 2014 at 15:09
  • $\begingroup$ Hi ! But this is the Mathematica, not the mathematics StackExchange. Plus, do use the comment dialog boxes or edit your post and not the answer system. $\endgroup$
    – Sektor
    Nov 2, 2014 at 15:49

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